## Maths AI Winter Revision Course 2022

Join our expert tutor, Yilmaz, as he provides you with Maths IB-Mock Revision Tuition. This is a two-day revision course on the five topics of the IB Mathematics AI for both SL and HL. These are Number & Algebra, Functions, Geometry & Trigonometry, Statistics, and Calculus. Students will be taken through the techniques of problem-solving using IB past papers. As this is for revision, lessons will be concise and focused on how to solve questions. It is expected that students will be able to approach standard IB questions after taking this course confidently.

Please see the detailed Curriculum breakdown below.

**Day 1: Number & Algebra, Functions, Geometry & Trigonometry: **

- Operation with numbers and standard form
- Arithmetic and geometric sequences and series with applications including amortizations and annuities
- System of linear equations and polynomials
- Logarithms and exponents
- Matrices and complex numbers
- Different forms of the equation of a straight line
- Concept of function, domain, range, and graph and their transformations
- Inverse and composite functions
- Linear, quadratic, cubic, sinusoidal, Logistic, and piecewise models
- Distance between two points in 3D, midpoint, volume, and surface area
- The angle between two intersecting lines or between a line and a plane
- Trigonometry and its application (sine rule, cosine rule, angle of elevation, and depression)
- Equation of perpendicular bisectors and Voronoi diagrams
- Length of an arc and area of a sector on a circle
- Geometric transformation and vectors
- Vector equation of a plane, scalar, and vector product
- Graph theory, adjacency matrices, and weighted adjacency tables
- Tree and cycle algorithms with undirected graphs

**Day 2: Statistics and Calculus: **

- Concept of population, sample, random sample, discrete and continuous data
- Presentation of data (frequency tables, histogram, cumulative frequency curves)
- The measure of central tendency and measure of variation
- Effect of constant changes on the original data
- Linear correlation and bivariate data
- Equation of regression line and its interpretation
- Regression with non-linear functions
- Probability
- Discrete probability distribution
- Binomial, Poisson and normal distribution
- Linear transformations of a single random variable
- Hypothesis testing (Chi-squared, test for population mean, test for proportion)
- Transition matrices and Markov chains
- Introduction to the concept of limit
- Derivative interpreted as a gradient function and as a rate of change
- Increasing and decreasing functions, Tangents, and normal
- Integration as an anti-differentiation
- Local maximum and minimum points
- Optimization problems
- Approximating areas using the trapezoidal rule
- Derivatives of trigonometric functions and second derivatives
- Definite and indefinite integrals
- Area under curves
- The volume of revolution about the x-axis or y-axis
- Kinematics problems involving displacement, velocity, and acceleration
- Differential equations
- Slope fields and their diagrams
- Euler’s method for finding the approximate solution to first-order differential equations
- Numerical solution of coupled differential equation
- Solution of second-order differential equation by Euler’s method and by finding exact solutions